If you look from enough of a distance, the answer is yes.
Close up, both will have their own developing wake. The boundary layer leaving wing and tail will leave a speed discontinuity, and the downward moving wing wake will be complemented by a tail wake which will slow down this downward movement directly behind the tail and increase it left and right of the central tail wake. Normally, the horizontal tails of transport aircraft produce a considerable downforce during landing to compensate for the backward shift of the center of pressure when the high lift devices are employed.
Aircraft model flying through illuminated smokescreen (picture source)
In the animated GIF above you can see the wake of the tail as a darker box inside the bigger wing wake. It forms two small vortices which rotate against the rotation direction of the wing wake and get spread out when being absorbed by the wing wake.
Friction will soon dissipate the much weaker tail wake, so at some distance all what is left is a single wake which will look slightly distorted around its center when compared to the wake of the isolated wing.
Fun fact: The negative lift on the tail can even contribute some thrust.